10.450 Process Dynamics, Operations, and Control Lecture Notes - 23 Lesson 23. Tuning a real controller - modeling, process identification, fine tuning 23.0 Context We have learned to view processes as dynamic systems, taking care to identify their input, intermediate, and output variables. We have learned that feedback can be used to control output variables, but can be misapplied to destabilize a system. We have discussed methods of tuning the PID control algorithm. Now we try it out on real equipment in the laboratory. 23.1 Tuning controllers, in the large view Quoting from Section 16.7: “In practice, we tune controllers in several stages: (0) develop a model of the process. Whether the model be simple or complicated, gather as much knowledge about the process as you can justify. (1) select the parameters based on the desired operating condition. Use an optimal control calculation, minimizing one of the integral error measures in calculated response, or apply an empirical tuning correlation. (2) adjust the parameters for plausible changes in conditions and uncertainties in the model. That is, repeat step (1) for several variations of the process model, and several conditions. Choose the parameters that give the best overall calculated response. (3) make fine-tuning adjustments in the field. Calculate the integral error measures from plant data. “Is there room for intuition in all this? Of course! We would be wrong to disparage the use of intuition in engineering work, just as we would be wrong to disparage modeling and analysis. In dealing with a complicated process, both the analog computation of instinct and the digital computation of mathematical models can be put to good use. “The key to all of this is to characterize our process as best we can. That means (1) description of desired state (2) understanding of behavior away from the desired state (3) clear idea of variables other than the controlled variable that are affected by transient response. The more we know about a process, the better we can devise suitable control for it.” 23.2 Identifying the process “Knowing the process” usually means some equation. We can get that equation through • Fundamental description: writing M&E balances on the equipment in the process. This quickly becomes impractical as the complexity of the process increases. • Identification: fitting a model (such as FODT, or an underdamped model) to experimental measurements of transient response. Stating this more carefully, we o propose that the process can be characterized by a particular transfer function. 110.450 Process Dynamics, Operations, and Control Lecture Notes - 23 o contrive a disturbance to the process and measure its transient response. o derive an equation to describe that response from the transfer function and the input disturbance. o compare the experimental data to the equation, adjusting parameters in the transfer function to fit the data. 23.3 A laboratory exercise in modeling and identification We have written balances for several simple processes in developing our understanding of dynamics and control. In the laboratory exercise, we will encounter a somewhat more complicated process that will illustrate several important points about dynamic systems, even before we consider the problem of tuning it! We will attempt to obtain process data in the lab, but first we will consider the M&E balance route. We begin with a P&I (piping and instrumentation) diagram of a heat exchanger demonstration rig; students use the rig to explore principles of heat transfer. It comprises a shell and tube heat exchanger; the hot stream recirculates through a heating tank, driven by a gear pump, and the cold stream flows once through to drain. TC FC TI TI FC Tho Thi Tco Tci Fh Q TI Fc The 10.302 student rightfully views the heat exchanger as the center of the process. However, the control problem (controlling temperature Thi by manipulating the electric heater in the tank) motivates a very different view of what comprises "the process". The development of a process model is summarized in the table; for illustration, it appears side-by-side with the simpler level control problem discussed previously. (You will probably find this table more useful if you review your notes in conjunction with the left column.) 210.450 Process Dynamics, Operations, and Control Lecture Notes - 23 Fd Fm • control liquid level h by manipulating inlet flow Fm • another inlet flow Fd is a disturbance TCFC TI TI FC ThoThi Tco Tci Fc Fh Q TI • control heat exchanger hot inlet temperature Thi by manipulating electric heater duty Q • disturbances include cold inlet temperature Tci, hot flow rate Fh, and cold flow rate Fc Identify input and output variables; assign these as controlled, manipulated, disturbance, or intermediate. ediate variables usually become more evident as the equations are written in the following step.) We do not yet know the equations that comprise the process model. process MV DV CVFm Fd h IV: Fo process MV DV DV DV CVQ Fh Fc Tci Thi IV: Tco, Tho The user of the heat exchanger cares most about the heat exchanger outlet temperatures Tho and Tco. problem, however, these are merely intermediate variables. Write M&E balances, with supplementary equations, as required. inate intermediate variables. inally obtain the differential equation that would lead to a solution of the form: CV = CV(DV,MV) • MB on tank: h = h(Fm, Fd, Fo) • MEB on tank: Fo = Fo(h) combine to obtain: • h = h(Fm, Fd) • EB on tank: Thi = Thi(Q, Fh, Tho) • EB on tube side: Tho = Tho(Thi, Tci, Tco, U, Fh) • EB on shell side: Tco = Tco(Thi, Tci, Tho, U, Fc) • Correlation: U = U(Fc, Fh) combine to obtain: • Thi = Thi(Q, Fh, Fc, Tci) For the user of the heat exchanger, the "process model" describes steady state heat transfer. , the "process model" (The intermIn the control ElimFBy contrast310.450 Process Dynamics, Operations, and Control Lecture Notes - 23 for control is a differential equation that relates transient behavior of the hot inlet temperature to independent disturbances. Express the model in deviation variables and take Laplace transforms. diagrams to represent the separate processes for each input variable. Remember that there is as yet no control: CV is best thought of as "the variable we intend to control". established the functional dependence of CV on each input. MV* DV* CV* F* m F* d